A function $g$ satisfies the property that $g(k) = 3k + 5$ for each of the 15 integer values of $k$ in $[1,15]$.
For each statement below, state if it is true or false.
(i) If $g(x)$ is a linear polynomial, then $g(x) = 3x + 5$.
(ii) $g$ cannot be a polynomial of degree 10.
(iii) $g$ cannot be a polynomial of degree 20.
(iv) If $g$ is differentiable, then $g$ must be a polynomial.

$P(x)$ and $Q(x)$ are non-constant polynomials, and $R(x)$ is a first-degree polynomial, where
$$P(x) = Q(x) \cdot R(x)$$
the equality is satisfied.
Accordingly, I. The constant terms of polynomials $P(x)$ and $R(x)$ are the same. II. If the graph of $P(x)$ is a parabola, then the graph of $Q(x)$ is a line. III. Every root of polynomial $Q(x)$ is also a root of polynomial $R(x)$. Which of the following statements are always true?
A) Only II
B) Only III
C) I and II
D) I and III
E) II and III